Decorated article

ABSTRACT

In a decorative object with a transparent body, the formation of strong colored reflections is made possible by a certain shaping of the body in conjunction with an absorption-free interference coating system on areas of the surface. In addition, the disappearance of color depth or saturation under ordinary lighting conditions is prevented.

BACKGROUND OF THE INVENTION

The invention relates to articles, the shape of which and the surface ofwhich are designed in a specific manner to achieve an aesthetic effect.

The invention relates especially to a decorated article which exhibits atransparent body which has a specific shape and on the surface of whicha layer system is provided to generate interference effects.

Technical applications for optical components are known andconventional. Examples are high-efficiency mirrors, filters and beamsplitters. A survey is included in H.A.M. Macloed, Thin Film OpticalDevices, in "Active and passive thin film devices", Academic Press 1978(hereafter, reference D1)

A number of components may be produced only with the aid of interferencelayers. It is possible to cultivate virtually all physicallynon-forbidden optical properties with the aid of interference layersystems. The possibilities extend from complete dereflection to a mirrorwhich reflects more strongly than a silver surface; from a narrow-bandtransmission filter to a band pass with steep edges. The dependence ofthe optical properties transmission T and reflection R upon thewavelength results in the fact that the layer system appears to becoloured. In particular, it is easy to achieve powerful, colouredreflection using interference layer systems; this is not possible or ispossible only with difficulty when using other means.

Conventional dyeing takes place by addition of substances which absorb aspecific wavelength range. The article then appears in the colour of thenon-absorbed wavelengths. This mechanism takes place mainly upon thetransmission of the light, scarcely at all in reflection. Absorbingcoloration is characterised in that a part of the light is destroyed. Anarticle coloured in this manner has a dark effect. The greater thepurity and depth of the colour, the more light must be absorbed and thedarker is the effect of the article. This effect makes itselfdisadvantageously noticeable especially in circumstances in which thecolour is to be employed as a decorative element to achieve an aestheticeffect. The absorption is a property of the substances employed, so thatthe available colours are limited by the number of appropriatesubstances. Since what is involved is absorbing coloration, as a rulethe mixing of various substances gives an impure mixed colour.

The application of absorption-free interference layer systems brings thefollowing advantages:

production of any desired clear colours is possible,

powerful, coloured reflection,

bright colours, no loss of light.

Nevertheless, the absorption-free interference layer systems have not todate been used for decoration. It is to be assumed that the decisivefactor concerning the non-use is the following: The colour effect ofabsorption-free interference layer systems shows a marked dependenceupon the illumination conditions. In particular, it is harmful for anapplication that the colour effects almost disappear under usual, partlyuniform illumination.

For explanatory purposes, the term "depth of colour" K will be used.Light of intensity I impinges upon the eye of the observer. The changein the intensity with the wavelength is of decisive importance to thecolour perception. Maximum intensity Imax, and minimum intensity, Imin,occur within the visible range of the spectrum. The functionK=(Imax-Imin)/Imin can be taken as a measure of the depth of colour,provided that the extreme values are not so close that the eyeintegrates with respect to the wavelength. In the event that theintensity does not fluctuate, Imax-Imin=0, the value 0 emerges for K. Infact, in this case the light appears white (colourless). The eye"measures" relatively, so that the ratio of intensities is computed inK. A large value of Imin reduces the value of K, so that it is takeninto consideration that a basic intensity existing at all wavelengths"whitens" the colour.

of the coloration of an article, the decoration of which consists in thecoloration, it is to be required that the colours become effective undermany illumination conditions.

1st case: pure reflection

In the case of pure reflection, layer systems and even single layers(lustres, soap bubbles) show great depth of colour. This is caused by alow value of Imin. It is not necessary to make any effort to achieveadequate depth of colour in reflection. However, pure reflection occursvery infrequently.

2nd case: pure transmission

In pure transmission, acceptable depth of colour can be achieved onlywith threefold layers (Table 1, below). It does not present anydifficulty to achieve any selectably great depth of colour by design ofthe layer system. Pure transmission occurs more frequently than purereflection. In most cases, it is sufficient to view a light sourcethrough the article. The brightness of a light source is, in comparisonwith the surroundings, frequently so great that to an approximation itis possible to refer to pure transmission.

3rd case: reflection and transmission at the same time.

In this case, the depth of colour is a function of the ratio of thecausative intensities. FIG. 1 shows a typical illumination. Atransparent article G, which exhibits an interference layer S, issituated above a base surface U (e.g.: the surface of a table) and isviewed obliquely from above (indicated by the eye symbol. FIG. 3 showsthe quantities which are employed for the computation of the intensityimpinging on the eye. The intensity is made up of intensity A incidentfrom the left, multiplied by the transmission T, and the intensity Bincident from the right, multiplied by the reflection R. ##EQU1## Table2 (below) shows the depth of colour K as a function of V and R for thecase concerning FIG. 1. The uncoated rear surface of the article isdisregarded. The maximum reflection 60%, 81%, 93%, 96% corresponds to 3,5, 7 and 9-fold layers (Table 1). It emerges from Table 2 that in thecase of uniform illumination of the base surface (A=B or V=1) the depthof colour is precisely zero. This entire disappearance of the colouralso occurs under real conditions; that is, irrespective of other lightsources and illumination conditions in the room, as long as only thebase surface is uniformly illuminated. Table 2 also shows the values ofK for non-uniform illumination. The average value of K at differingvalues of V is a measure of the decorative effect under customaryillumination conditions. It is of interest that the average value of Kcannot be substantially increased by using a large number of layers.

The fact that the colour is weak under customary illumination conditionsand can in some cases entirely disappear is a considerable defect whichprevents the use of interference layers for the imparting of colour.Awareness of this defect forms part of the state of knowledge. Variousproposals were made for the purpose of alleviating the defect:

European Patent Application, Appl. No.: 85304031.9, Publ. No.: 0 165 021(hereafter reference D2) and

DE-OS 3635567 (hereafter reference D3).

A symbol-generating optical interference device for authenticityverification is propose in reference D2. The danger that theinterference colours are not visible is to be prevented in that entirelayer systems are applied one on top of the other. In fact, the averagedepth of colour increases with an increasing number of layers(increasing maximum reflection) to some extent, see Table 2. However, agreat expenditure is made for this purpose. The production expenditureincreases excessively with the number of layers, because layer defectsare additive. The gain in depth of colour is very small. Even with anarbitrarily large number of layers, the colour cannot be prevented fromentirely disappearing under uniform illumination (V=1).

Reference D3 is based on the observation that even low depths of colourare sufficient for decoration if it is ensured that different coloursare viewed at the same time. What takes place is an intensification ofthe contrast, and thus of the decorative effect, where two differentcolours are compared with one another; even where the respective depthof colour is very low. However, the specification according to referenceD3 presumes a non-disappearing depth of colour. In the event of uniformillumination, all colours disappear, so that in the circumstances it isno longer possible to make any comparison of different colours.Furthermore, the excessively low depth of colour in the vicinity of V=1can scarcely be alleviated by the specification according to referenceD3.

SUMMARY OF THE INVENTION

The object of the invention is to provide an article which with the aidof a layer system and of a transparent body

(1) exhibits the advantages of absorption-free coloration, in particulardevelops powerful colour reflections, permits any selectable colourchoice and makes possible bright coloration without loss of light and

(2) overcomes the defect of low or entirely disappearing depth of colourunder customary illumination.

According to the invention, the object is achieved in that

(a) the layer system comprises a sequence of at least three interferencelayers of varying refractive index,

(b) the surface of the transparent body is designed so that surfaceregions are present, the surface normals to which differ in all threespatial components,

(c) the layer system is disposed directly on the surface regions and

(d) the transparent body is designed in such a manner that in thecustomary position of use of the body at least one coated surface regioncan be viewed through a second coated surface region.

BRIEF DESCRIPTION OF THE DRAWINGS

FIG. 1 is a side view schematically illustrating a flat article with aninterference layer system, and light rays which reach the eye of anobserver after impinging on the article;

FIG. 2 is a side view schematically illustrating a U-shaped article withan interference layer system, and light rays which reach the eye of anobserver after impinging on the article;

FIG. 3 schematically illustrates light rays which are reflected andtransmitted by the interference layer system in FIG. 1;

FIG. 4 schematically illustrates light rays which are reflected andtransmitted by the interference layer system in FIG. 2;

FIG. 5 is a sectional view schematically illustrating a champagne glasswith an interference layer system, and light rays which reach the eye ofan observer after impinging on the champagne glass;

FIG. 6 is a graph showing the results of calculations made for secondorder reflection according to FIG. 5; and

FIG. 7 schematically illustrates a top plan view of the champagne glassof FIG. 5, with supplementary lines added to facilitate discussion.

DETAILED DESCRIPTION

The specification according to the invention sets in motion twoindependent physical mechanism. One mechanism attends to the creation ofcoloured reflections, and the second mechanism intensifies the depth ofcolour and also prevents the entire disappearance of the colour undercustomary illumination conditions.

The core of the invention is only accessible to experimentalmeasurements or mathematical analysis. This is so because at firstglance it cannot be understood how a layer which appears to becolourless then appears to be coloured when viewed through a secondlayer which likewise appears to be colourless.

In order to create the coloured reflections, it is necessary that thesurface normals are varied in all three spatial components, and that alayer is viewed through another layer, while to intensify the depth ofcolour it is alone sufficient that one layer is viewed through the otherlayer

Mechanism 1: Intensification of the depth of colour, prevention ofdisappearance of the colour under customary illumination

FIG. 2 shows the case in which an article G is situated on a basesurface U and is viewed obliquely from above. In contrast to FIG. 1(previously discussed in the "Background of the Invention" section),according to the invention the article exhibits two coated surfaceregions. FIG. 4 indicates the quantities which are employed for thecomputation of the intensity. With T as transmission and R asreflection, the intensity is given as ##EQU2##

It becomes clear that no value of V can be found for which the intensityI becomes independent of R. This means that according to the arrangementof FIG. 2 there is no illumination condition for which the colours ofthe arrangement disappear. Over and above this, Table 3 (below) showsthat the depth of colour is on average intensified. For example, thisdepth of colour is even for a threefold layer (Rmax=60%) greater thanfor a ninefold layer (Rmax=96%) according to Table 2.

Mechanism 2: Creation of coloured reflections and illustrativeembodiment

FIG. 5 shows an article G, for example a glass body with a curvedsurface (champagne glass), to the chalice walls of which a layer systemS has been applied. An observer, indicated by the eye symbol, views thearticle obliquely from above. At the position C he views a reflection ifa light source is also situated obliquely above. This is very easilypossible by means of a lamp, a bright room ceiling, a window or by thesky. What is involved is a second order reflection which is madepossible only in that the x and z components of the surface normals atvarious surface regions of the layer alter. For the relatively simplecase of a second order reflection according to FIG. 5, a computation wasmade. The case concerned involves oblique light incidence, so that s andp components of the light must be taken into consideration. The beampath is situated only in one plane, so that s and p components do notbecome converted into one another, and it is sufficient to treat s and pcomponents separately throughout the beam path. Specified data for thecomputation; threefold layer, transmission twice through the layersystem at an angle of incidence of 60°, reflection twice at an angle ofincidence of 30°, the uncoated substrate surfaces being disregarded.There are in existence mathematically favourably formulatedrepresentations of the interference effects in thin layers, for example,reference D1, pages 326--334, which can be utilised for the computationof the intensity. The results of the computation and the precise data onthe layersystem are presented in FIG. 6. As is evident from FIG. 6, theinvention permits

1. a considerable depth of colour, even for the simplest layer systemand

2. a surprisingly high value for Imax.

The high value of Imax arises as a result of the use of the angledependence of the optical properties of interference layer systems. Ifthe optical properties were independent of the angle of incidence, thenImax=6.25% would emerge after transmission twice and reflection twice.The value of approximately 30% for Imax emerging from FIG. 6 relates tothe intensity of the obliquely incident light. As a rule, the effect ofthe reflection is greater than the computed value permits to be assumed.For a reflection from a light source of high illumination density may beinvolved, or alternatively the light of an angular range is collectedand concentrated onto the eye of the observer. Such concentration isindicated in FIG. 5 by three beam paths. The occurrence of thereflection is not tied to the specific geometry of FIG. 5. Thereflection also occurs at other angles of incidence and angles of view.The angle of incidence and the angle of view do not need to be equallylarge. The reflection is then displaced in height on the glass. That isto say, there is frequently an entire reflection line under customaryillumination.

To date, consideration has been given to the second order reflection.However, according to the arrangement according to the inventionreflections of higher order also occur. To view these, it is necessaryto take into account all three spatial components of the beam path. Thearticle shown in FIG. 5 is considered to be rotationally symmetric withrespect to the z axis. In these circumstances, a representationaccording to FIG. 7 (top plan view) emerges for the x-y plane. In asimilar way to FIG. 5, the incident beam is deflected in the lower partof the chalice. The radius of the chalice is small there, correspondingto R1 in FIG. 7. In the upper part, the chalice constantly has theradius R2. FIG. 7 shows a threefold reflection. It is characteristicthat all rays within the chalice are tangent to a circle having theradius RB. The conditions

    1φ+4θ=180°, RB/R1=sin φ and RB/R2=sin θ

give with precision a physically meaningful solution

    RB=-R2.sup.2 /4R1+√(R2.sup.2 /4R1).sup.2 +R2.sup.2 /2.

That is to say, from the point of view of the observer, the third orderreflection appears at a definite spacing from the second orderreflection. If the causative light source does not have excessivelylarge dimensions, the reflections are sharply separated from oneanother. Likewise, reflections of higher order are observed which areclearly separated from one another.

If the angle of incidence covers a whole range, then all orders formreflection lines.

The creation of these reflections is not trivial. Such creation requiresthe cooperation, according to the invention, of an interference layersystem with a specific shaping. It is necessary for the surface normalsin all three spatial components to vary. A transparent article of shapeaccording to the invention can indeed form higher order reflections evenwithout an interference layer. However, the intensity of thesereflections is so low that observation is difficult and use fordecoration of the article would be well nigh impossible.

The differences in the intensity are drastic. For example, the followingvalues for the intensity of the second order reflection emerge for thebeam path according to FIG. 5 in the absence of the interference layersystem:

p-component: 0.0731%

s-component: 0.250%

computed in each case for a glass-air interface. Compared with the valueof Imax from FIG. 6 amounting to approximately 30%, in this case theintensity is reduced to values which are in some cases far less than onehundredth. The difference permits the formulation that such reflectionsof higher order appear only as a result of the arrangement according tothe invention.

The arrangement according to the invention is very suitable for thedecoration of transparent articles. The reflections created generate theimpression of being "highly sparkling" to an extent not known hitherto.

                  TABLE 1                                                         ______________________________________                                                                      Depth of colour K                                             Rmax    Rmin    for transmission                                Layer system  in %    in %    viewing                                         ______________________________________                                        S H           30.64   4.25    0.380                                           S H N H       61.18   4.25    1.466                                           S H N H N H   81.21   4.25    4.095                                           S H N H N H N H                                                                             91.53   4.25    10.304                                          S H N H N H N H N H                                                                         96.30   4.25    24.878                                          ______________________________________                                         K = (ImaxImin)/Imin = (RmaxRmin)/(1-Rmax) for transmission viewing            S: Substrate, refractive index 1.52, absorptionfree                           H: Highrefraction lambda/4 layer, absorptionfree, refractive index 2.3        N: Lowrefraction lambda/4 layer, absorptionfree, refractive index 1.5         normal light incidence                                                        Rmax: maximum reflection (wavelength equal to lambda)                         Rmin: minimum reflection (within the entire wavelength range)            

                                      TABLE 2                                     __________________________________________________________________________    I = (1 - R) + VR                                                              K(Rmax) = (Imax - Imin)/Imin for O < R < Rmax                                 R in %                                                                             V = 0.50                                                                           V = 0.60                                                                           V = 0.70                                                                           V = 0.80                                                                           V = 0.90                                                                           V = 1.00                                                                           V = 1.10                                                                           V = 1.20                                                                            V = 1.30                                                                           V = 1.40                   __________________________________________________________________________     0   100.00                                                                             100.00                                                                             100.00                                                                             100.00                                                                             100.00                                                                             100.00                                                                             100.00                                                                             100.00                                                                              100.00                                                                             100.00                      3   98.50                                                                              98.80                                                                              99.10                                                                              99.40                                                                              99.70                                                                              100.00                                                                             100.30                                                                             100.60                                                                              100.90                                                                             101.20                      6   97.00                                                                              97.60                                                                              98.20                                                                              98.80                                                                              99.40                                                                              100.00                                                                             100.60                                                                             101.20                                                                              101.80                                                                             102.40                      9   95.50                                                                              96.40                                                                              97.30                                                                              98.20                                                                              99.10                                                                              100.00                                                                             100.90                                                                             101.80                                                                              102.70                                                                             103.60                     12   94.00                                                                              95.20                                                                              96.40                                                                              97.60                                                                              98.80                                                                              100.00                                                                             101.20                                                                             102.40                                                                              103.60                                                                             104.80                     15   92.50                                                                              94.00                                                                              95.50                                                                              97.00                                                                              98.50                                                                              100.00                                                                             101.50                                                                             103.00                                                                              104.50                                                                             106.00                     18   91.00                                                                              92.80                                                                              94.60                                                                              96.40                                                                              98.20                                                                              100.00                                                                             101.80                                                                             103.60                                                                              105.40                                                                             107.20                     21   89.50                                                                              91.60                                                                              93.70                                                                              95.80                                                                              97.90                                                                              100.00                                                                             102.10                                                                             104.20                                                                              106.30                                                                             108.40                     24   88.00                                                                              90.40                                                                              92.80                                                                              95.20                                                                              97.60                                                                              100.00                                                                             102.40                                                                             104.80                                                                              107.20                                                                             109.60                     27   86.50                                                                              89.20                                                                              91.90                                                                              94.60                                                                              97.30                                                                              100.00                                                                             102.70                                                                             105.40                                                                              108.10                                                                             110.80                     30   85.00                                                                              88.00                                                                              91.00                                                                              94.00                                                                              97.00                                                                              100.00                                                                             103.00                                                                             106.00                                                                              109.00                                                                             112.00                     33   83.50                                                                              86.80                                                                              90.10                                                                              93.40                                                                              96.70                                                                              100.00                                                                             103.30                                                                             106.60                                                                              109.90                                                                             113.20                     36   82.00                                                                              85.60                                                                              89.20                                                                              92.80                                                                              96.40                                                                              100.00                                                                             103.60                                                                             107.20                                                                              110.80                                                                             114.40                     39   80.50                                                                              84.40                                                                              88.30                                                                              92.20                                                                              96.10                                                                              100.00                                                                             103.90                                                                             107.80                                                                              111.70                                                                             115.60                     42   79.00                                                                              83.20                                                                              87.40                                                                              91.60                                                                              95.80                                                                              100.00                                                                             104.20                                                                             108.40                                                                              112.60                                                                             116.80                     45   77.50                                                                              82.00                                                                              86.50                                                                              91.00                                                                              95.50                                                                              100.00                                                                             104.50                                                                             109.00                                                                              113.50                                                                             118.00                     48   76.00                                                                              80.80                                                                              85.60                                                                              90.40                                                                              95.20                                                                              100.00                                                                             104.80                                                                             109.60                                                                              114.40                                                                             119.20                     51   74.50                                                                              79.60                                                                              84.70                                                                              89.80                                                                              94.90                                                                              100.00                                                                             105.10                                                                             110.20                                                                              115.30                                                                             120.40                     54   73.00                                                                              78.40                                                                              83.80                                                                              89.20                                                                              94.60                                                                              100.00                                                                             105.40                                                                             110.80                                                                              116.20                                                                             121.60                     57   71.50                                                                              77.20                                                                              82.90                                                                              88.60                                                                              94.30                                                                              100.00                                                                             105.70                                                                             111.40                                                                              117.10                                                                             122.80                     60   70.00                                                                              76.00                                                                              82.00                                                                              88.00                                                                              94.00                                                                              100.00                                                                             106.00                                                                             112.00                                                                              118.00                                                                             124.00                     63   68.50                                                                              74.80                                                                              81.10                                                                              87.40                                                                              93.70                                                                              100.00                                                                             106.30                                                                             112.60                                                                              118.90                                                                             125.20                     66   67.00                                                                              73.60                                                                              80.20                                                                              86.80                                                                              93.40                                                                              100.00                                                                             106.60                                                                             113.20                                                                              119.80                                                                             126.40                     69   65.50                                                                              72.40                                                                              79.30                                                                              86.20                                                                              93.10                                                                              100.00                                                                             106.90                                                                             113.80                                                                              120.70                                                                             127.60                     72   64.00                                                                              71.20                                                                              78.40                                                                              85.60                                                                              92.80                                                                              100.00                                                                             107.20                                                                             114.40                                                                              121.60                                                                             128.80                     75   62.50                                                                              70.00                                                                              77.50                                                                              85.00                                                                              92.50                                                                              100.00                                                                             107.50                                                                             115.00                                                                              122.50                                                                             130.00                     78   61.00                                                                              68.80                                                                              76.60                                                                              84.40                                                                              92.20                                                                              100.00                                                                             107.80                                                                             115.60                                                                              123.40                                                                             131.20                     81   59.50                                                                              67.60                                                                              75.70                                                                              83.80                                                                              91.90                                                                              100.00                                                                             108.10                                                                             116.20                                                                              124.30                                                                             132.40                     84   58.00                                                                              66.40                                                                              74.80                                                                              83.20                                                                              91.60                                                                              100.00                                                                             108.40                                                                             116.80                                                                              125.20                                                                             133.60                     87   56.50                                                                              65.20                                                                              73.90                                                                              82.60                                                                              91.30                                                                              100.00                                                                             108.70                                                                             117.40                                                                              126.10                                                                             134.80                     90   55.00                                                                              64.00                                                                              73.00                                                                              82.00                                                                              91.00                                                                              100.00                                                                             109.00                                                                             118.00                                                                              127.00                                                                             136.00                     93   53.50                                                                              62.80                                                                              72.10                                                                              81.40                                                                              90.70                                                                              100.00                                                                             109.30                                                                             118.60                                                                              127.90                                                                             137.20                     96   52.00                                                                              61.60                                                                              71.20                                                                              80.80                                                                              90.40                                                                              100.00                                                                             109.60                                                                             119.20                                                                              128.80                                                                             138.40                     99   50.50                                                                              60.40                                                                              70.30                                                                              80.20                                                                              90.10                                                                              100.00                                                                             109.90                                                                             119.80                                                                              129.70                                                                             139.60                                                                              Average K            K (60%)                                                                            0.428                                                                              0.315                                                                              0.219                                                                              0.136                                                                              0.063                                                                              0.000                                                                              0.060                                                                              0.120 0.180                                                                              0.240 0.176                K (81%)                                                                            0.680                                                                              0.479                                                                              0.321                                                                              0.193                                                                              0.088                                                                              0.000                                                                              0.081                                                                              0.162 0.243                                                                              0.324 0.257                K (93%)                                                                            0.869                                                                              0.592                                                                              0.386                                                                              0.228                                                                              0.102                                                                              0.000                                                                              0.093                                                                              0.186 0.279                                                                              0.372 0.310                K (96%)                                                                            0.923                                                                              0.623                                                                              0.404                                                                              0.237                                                                              0.106                                                                              0.000                                                                              0.096                                                                              0.192 0.288                                                                              0.384 0.325                __________________________________________________________________________

                                      TABLE 3                                     __________________________________________________________________________    I = (1 - R).sup.2 + V(1 - R).sup.2 + R)                                       K(Rmax) = (Imax - Imin)/Imin for O < R < Rmax                                 R in %                                                                             V = 0.50                                                                           V = 0.60                                                                           V = 0.70                                                                           V = 0.80                                                                           V = 0.90                                                                           V = 1.00                                                                           V = 1.10                                                                           V = 1.20                                                                            V = 1.30                                                                           V = 1.40                   __________________________________________________________________________     0   100.00                                                                             100.00                                                                             100.00                                                                             100.00                                                                             100.00                                                                             100.00                                                                             100.00                                                                             100.00                                                                              100.00                                                                             100.00                      3   97.00                                                                              97.58                                                                              98.16                                                                              98.74                                                                              99.33                                                                              99.91                                                                              100.49                                                                             101.07                                                                              101.65                                                                             102.24                      6   94.01                                                                              95.14                                                                              96.27                                                                              97.40                                                                              98.53                                                                              99.66                                                                              100.79                                                                             101.92                                                                              103.05                                                                             104.18                      9   91.03                                                                              92.68                                                                              94.32                                                                              95.97                                                                              97.61                                                                              99.26                                                                              100.90                                                                             102.55                                                                              104.19                                                                             105.84                     12   88.08                                                                              90.21                                                                              92.34                                                                              94.47                                                                              96.60                                                                              98.73                                                                              100.86                                                                             102.99                                                                              105.12                                                                             107.24                     15   85.16                                                                              87.75                                                                              90.33                                                                              92.92                                                                              95.50                                                                              98.08                                                                              100.67                                                                             103.25                                                                              105.83                                                                             108.42                     18   82.29                                                                              85.30                                                                              88.31                                                                              91.32                                                                              94.33                                                                              97.34                                                                              100.35                                                                             103.36                                                                              106.37                                                                             109.38                     21   79.46                                                                              82.87                                                                              86.28                                                                              89.69                                                                              93.10                                                                              96.51                                                                              99.92                                                                              103.33                                                                              106.74                                                                             110.15                     24   76.69                                                                              80.47                                                                              84.26                                                                              88.04                                                                              91.83                                                                              95.62                                                                              99.40                                                                              103.19                                                                              106.98                                                                             110.76                     27   73.98                                                                              78.12                                                                              82.26                                                                              86.40                                                                              90.53                                                                              94.67                                                                              98.81                                                                              102.95                                                                              107.09                                                                             111.23                     30   71.35                                                                              75.82                                                                              80.29                                                                              84.76                                                                              89.23                                                                              93.70                                                                              98.17                                                                              102.64                                                                              107.11                                                                             111.58                     33   68.79                                                                              73.57                                                                              78.35                                                                              83.14                                                                              87.92                                                                              92.70                                                                              97.48                                                                              102.26                                                                              107.04                                                                             111.82                     36   66.33                                                                              71.40                                                                              76.48                                                                              81.55                                                                              86.63                                                                              91.70                                                                              96.78                                                                              101.85                                                                              106.92                                                                             112.00                     39   63.96                                                                              69.31                                                                              74.66                                                                              80.01                                                                              85.37                                                                              90.72                                                                              96.07                                                                              101.42                                                                              106.77                                                                             112.12                     42   61.70                                                                              67.31                                                                              72.93                                                                              78.54                                                                              84.15                                                                              89.76                                                                              95.38                                                                              100.99                                                                              106.60                                                                             112.22                     45   59.55                                                                              65.41                                                                              71.27                                                                              77.14                                                                              83.00                                                                              88.86                                                                              94.72                                                                              100.58                                                                              106.44                                                                             112.30                     48   57.52                                                                              63.62                                                                              69.72                                                                              75.82                                                                              81.92                                                                              88.01                                                                              94.11                                                                              100.21                                                                              106.31                                                                             112.41                     51   55.63                                                                              61.95                                                                              68.28                                                                              74.60                                                                              80.93                                                                              87.25                                                                              93.57                                                                              99.90 106.22                                                                             112.55                     54   53.87                                                                              60.41                                                                              66.95                                                                              73.50                                                                              80.04                                                                              86.58                                                                              93.12                                                                              99.67 106.21                                                                             112.75                     57   52.25                                                                              59.01                                                                              65.76                                                                              72.52                                                                              79.27                                                                              86.02                                                                              92.78                                                                              99.53 106.29                                                                             113.04                     60   50.80                                                                              57.76                                                                              64.72                                                                              71.68                                                                              78.64                                                                              85.60                                                                              92.56                                                                              99.52 106.48                                                                             113.44                     63   49.50                                                                              56.66                                                                              63.82                                                                              70.98                                                                              78.15                                                                              85.31                                                                              92.47                                                                              99.63 106.80                                                                             113.96                     66   48.37                                                                              55.73                                                                              63.10                                                                              70.46                                                                              77.82                                                                              85.18                                                                              92.55                                                                              99.91 107.27                                                                             114.64                     69   47.42                                                                              54.98                                                                              62.55                                                                              70.11                                                                              77.67                                                                              85.24                                                                              92.80                                                                              100.36                                                                              107.93                                                                             115.49                     72   46.66                                                                              54.42                                                                              62.19                                                                              69.95                                                                              77.72                                                                              85.48                                                                              93.24                                                                              101.01                                                                              108.77                                                                             116.54                     75   46.09                                                                              54.06                                                                              62.03                                                                              70.00                                                                              77.96                                                                              85.93                                                                              93.90                                                                              101.87                                                                              109.84                                                                             117.81                     78   45.72                                                                              53.90                                                                              62.08                                                                              70.26                                                                              78.43                                                                              86.61                                                                              94.79                                                                              102.97                                                                              111.14                                                                             119.32                     81   45.57                                                                              53.96                                                                              62.35                                                                              70.74                                                                              79.14                                                                              87.53                                                                              95.92                                                                              104.31                                                                              112.71                                                                             121.10                     84   45.63                                                                              54.25                                                                              62.86                                                                              71.48                                                                              80.09                                                                              88.71                                                                              97.32                                                                              105.94                                                                              114.55                                                                             123.17                     87   45.92                                                                              54.77                                                                              63.61                                                                              72.46                                                                              81.31                                                                              90.16                                                                              99.00                                                                              107.85                                                                              116.70                                                                             125.54                     90   46.45                                                                              55.54                                                                              64.63                                                                              73.72                                                                              82.81                                                                              91.90                                                                              100.99                                                                             110.08                                                                              119.17                                                                             128.26                     93   47.21                                                                              56.56                                                                              65.90                                                                              75.25                                                                              84.60                                                                              93.94                                                                              103.29                                                                             112.63                                                                              121.98                                                                             131.32                     96   48.23                                                                              57.85                                                                              67.46                                                                              77.08                                                                              86.69                                                                              96.31                                                                              105.92                                                                             115.54                                                                              125.15                                                                             134.77                     99   49.51                                                                              59.41                                                                              69.31                                                                              79.21                                                                              89.11                                                                              99.01                                                                              108.92                                                                             118.72                                                                              128.72                                                                             138.62                                                                              Average K            K (60%)                                                                            0.968                                                                              0.731                                                                              0.545                                                                              0.395                                                                              0.271                                                                              0.168                                                                              0.090                                                                              0.038 0.071                                                                              0.134 0.341                K (81%)                                                                            1.194                                                                              0.855                                                                              0.612                                                                              0.429                                                                              0.287                                                                              0.173                                                                              0.091                                                                              0.048 0.127                                                                              0.211 0.402                K (93%)                                                                            1.194                                                                              0.855                                                                              0.612                                                                              0.429                                                                              0.287                                                                              0.173                                                                              0.116                                                                              0.131 0.219                                                                              0.313 0.433                K (96%)                                                                            1.194                                                                              0.855                                                                              0.612                                                                              0.429                                                                              0.287                                                                              0.173                                                                              0.145                                                                              0.161 0.251                                                                              0.347 0.445                __________________________________________________________________________

I claim:
 1. A decorated article, comprising:a transparent body withoutan internal light source, the body having a customary position of use,the body additionally having a surface with surface regions that areoriented so that a first unit vector normal to a first one of thesurface regions has X, Y, and Z components and a second unit vectornormal to a second one of the surface regions has X, Y, and Z componentsthat differ from those of the first unit vector for each of the X, Y,and Z components; and a layer system on the surface of the body andcovering at least said first one of the surface regions and said secondone of the surface regions, the layer system including a sequence of atlest three interference layers of varying refractive index, wherein thebody is configured in such a manner that, in its customary position ofuse, at least a portion of the layer system covering said second one ofthe surface regions can be viewed through a portion of the layer systemcovering said first one of the surface regions.
 2. A decorated articleaccording to claim 1, wherein the layer system comprises a layer, therefractive index of which constantly varies in a direction normal to thesurface of the body, which layer can be considered, to an approximation,as a sequence of at least three layers of varying refractive index.
 3. Adecorated article according to claim 2, wherein the layer systemexhibits differing optical properties on different surface regions.
 4. Adecorated article according to claim 1, wherein the layer systemexhibits differing optical properties on different surface regions.
 5. Adecorated article, comprising:a light-permeable body without an internallight source, the body having a surface with surface regions that areoriented so thata first unit vector normal to a first one of the surfaceregions has X, Y, and Z components, a second unit vector normal to asecond one of the surface regions has X, Y, and Z components that differfrom those of the first unit vector for each of the X, Y, and Zcomponents, and a third unit vector normal to a third one of the surfaceregions has X, Y, and Z components that differ from those of the firstand second unit vectors for each of the X, Y, and Z components; and alayer system on the surface of the body and covering said first one ofthe surface regions, said second one of the surface regions, and saidthird one of the surface regions, the layer system including at leastone interference layer; wherein the body is configured in such a mannerthat a ray of light reflected from a portion of the layer systemcovering said third one of the surface regions and then reflected from aportion of the layer system covering said second one of the surfaceregions is visible through a portion of the layer system covering saidfirst one of the surface regions.
 6. A decorative article according toclaim 5, wherein the layer system includes a sequence of at lest threeinterference layers of varying refractive index.
 7. A decorative articleaccording to claim 5, wherein the layer system comprises a layer, therefractive index of which constantly varies in a direction normal to thesurface of the body, which layer can be considered, to an approximation,as a sequence of at lest three layers of varying refractive index.
 8. Adecorative article according to claim 5, wherein the body is a drinkingvessel having a wall, and wherein said first one of the surface regions,said second one of the surface regions, and said third one of thesurface regions are provided at spaced apart positions on the wall ofthe drinking vessel.